It begins from an inferentialist, and particularly bilateralist, theory of meaning--one which takes meaning to be constituted by assertibility and deniability conditions--and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance.

It presupposes a good knowledge of classical logic and its model-theory, and also familiarity with the preferential semantics for systems of uncertain (aka nonmonotonic) consequence.

Imagine, for example, that we simply translated the recursive definition of theoremhood for some axiom system for classical logic into a correspondingly recursive definition on the model-theoretic level, and then restate and prove the completeness theorem for classical logic in terms of that translation.

The first concerns many-valued deductive logics that have monotony or antitony properties including, as a limiting case, classical logic.

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